HSPA: High-Throughput Sparse Polynomial Multiplication for Code-based Post-Quantum Cryptography

Abstract

Increasing attention has been paid to code-based post-quantum cryptography (PQC) schemes, e.g., HQC (Hamming Quasi-Cyclic) and BIKE (Bit Flipping Key Encapsulation), since they’ve been selected as the fourth-round National Institute of Standards and Technology (NIST) PQC standardization candidates. Though sparse polynomial multiplication is one of the critical components for HQC and BIKE, hardware-implemented high-performance sparse polynomial multiplier is rarely reported in the literature (due to its high-dimension and sparsity of polynomials involved in the computation). Based on this consideration, in this article, we propose two novel H igh-throughput S parse P olynomial multiplication A ccelerators (HSPA) for the mentioned two code-based PQC schemes. Specifically, we have designed the two accelerators based on two different implementation strategies targeting potential applications with different resource availability, i.e., one accelerator deploys a memory-based structure for computation while the other does not need memory usage. We have proposed three layers of coherent interdependent efforts to obtain the proposed accelerators. First, we have proposed two implementation strategies to execute the targeted sparse polynomial multiplication, i.e., a new parallel segment based accumulation (PSA) approach and a novel permutating-with-power (PWP)-based method. Then, the proposed two hardware accelerators are presented with detailed structural descriptions. Finally, field-programmable gate array (FPGA)-based implementation is presented to showcase the superior performance of the proposed accelerators. A proper comparison is also carried out to confirm the efficiency of the proposed designs. For instance, the proposed accelerator (using memory-based structure) has 56.84% and 80.25% less area-delay product (ADP) than the existing memory-based design (an extended high-speed version) on the UltraScale+ device, respectively, for n =17,669 and ω =75 (HQC) and n = 12,323 and ω =142 (BIKE). The proposed design strategy fits well with the two targeted code-based PQC schemes, which can be extended further to construct high-performance hardware cryptoprocessors. We hope the results of this work will be useful for the ongoing NIST PQC standardization process.